412 APPLIED MECHANICS 
next 2 inches of the cam stroke the follower rises 14 inches with uniform re- 
tardation, and then remains at rest until the cam has completed its forward 
stroke. The follower is provided with a roller 1} inches in diameter, which 
works on the cam. Draw the outline of the cam. ; 
2. Same as Exercise 1, except that the cam has simple harmonic motion, 
instead of uniform motion. 
3. A straight lever oscillates in the plane of a sliding cam, about an axis at 
one end, though angles of 29° on opposite sides of a line parallel to the line of — 
stroke of the cam. The lever has simple harmonic motion, and one complete 
oscillation of the lever is performed during two strokes of the cam. The stroke 
of the cam is 5 inches. The cam works against a roller 1 inch in diameter, 
whose axis is at the free end of the lever and 6 inches from the axis about 
which the lever swings. Assuming that the cam has uniform motion, draw its 
contour. 
4. Same as Exercise 3, except that the cam has simple harmonic motion, 
instead of uniform motion. 
5. Draw the profile of a cam to do the following work :—It has to lift a bar 
vertically with uniform velocity, the length of the travel of the bar being 6 
inches; it then has to allow the bar to descend again with uniform velocity, 
but at one half the speed of the ascent. The two movements occupy one 
revolution of the uniformly rotating cam. The diameter of the roller working 
on the cam is $ inch, and the least thickness of metal round the cam centre 
must be 2 inches. The line of stroke of the moving bar passes through the 
cam centre. [B.E.] 
6. Set out the form of a plane cam, rotating with uniform velocity, to give a 
bar reciprocating motion of the following character. During each stroke the 
bar is to have simple harmonic motion. ‘The out stroke is to be performed while 
the cam makes one-half of a revolution, and the in stroke while the cam makes 
one-third of a revolution. There are to be equal periods of rest at each end of 
the stroke. Stroke of bar, 3 inches. Line of stroke, $ inch to one side of axis of 
cam. Diameter of roller which works on cam, 1 inch. Minimum distance be- 
tween axis of cam and axis of roller, 2 inches. If the cam makes 30 revolutions 
per minute, what is the maximum speed of the bar, in feet per minute, (a) 
during the out stroke, (5) during the in stroke? : 
7. O is the axis about which an arm OA swings. OA=3'5inches. A is the 
axis of a roller, 0°5 inch in diameter, carried by the arm, and this roller works 
against a cam which rotates with uniform velocity, and whose axis C is 4 inches 
from O. The greatest and least distances of A from C are 3°5 inches and 1°25 
inches respectively. Design the cam so that the arm shall have uniform 
angular velocity when swinging, and periods of rest at each end of the swing 
corresponding to one-twelfth of a revolution of the cam. 
8. A cam mechanism is shown in Fig. 674. The cam C rotates uniformly 
about O, and actuates the slider S by 
means of the bent lever LL. The slider 
has an intermittent motion as follows: 
(a) A period of rest while the cam turns 
through 150°. (5) The upward half of 
a simple harmonic motion from A to B- 
while the cam turns through the next 
129°. (c) The downward half of another 
simple harmonic motion while the cam 
turns through 90°. Set out the true 
shape of the cam profile, working to the 
given dimensions and not copying the 
diagram. [B.E.] 
9. A vertical bar with a flat horizon- 
tal foot (see Fig. €31, p. 397) is driven 
upwards with simple harmonic motion, 
and lowered with uniform acceleration, Fic. 674. 
by a cam mounted on a _ horizontal 
shaft, and having uniform angular velocity. The up stroke of the bar is per- 
formed while the cam turns through an angle of 180°, and the down stroke 
while the cam turns through an angle of 90°. The bar is at rest at the bottom 
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